**Chapter 3 Playing With Numbers Ex. 3.6**

Question 1.

Find the HCF of the following numbers:

(a) 18, 48

(b) 30, 42

(c) 18, 60

(d) 27,63

(e) 36,84

(f) 34, 102

(g) 70, 105, 175

(h) 91, 112, 49

(i) 18, 54, 81

(j) 12, 45, 75

Solution:

Question 2.

What is the HCF of two consecutive

(a) numbers?

(b) even numbers?

(c) odd numbers?

Solution:

(a) The common factor of two consecutive numbers is always 1.

Hence, the HCF = 1.

(b) The common factors of two consecutive even numbers are 1 and 2.

Hence, the HCF = 1 x 2 = 2.

(c) The common factor of two consecutive odd numbers is 1.

Hence, the HCF = 1.

Question 3.

HCF of co-prime numbers 4 and 15 was found as follows by factorisation:

4 = 2 x 2 and 15 = 3 x 15. Since there is no common prime factors, so HCF of 4 and 15 is 0.

Is the answer correct? If not, what is the correct HCF?

Solution:

No, answer is not correct.

Reason: 0 is not the prime factor of any number.

1 is always the prime factor of co-prime number.

Hence, the correct HCF of 4 and 15 is 1.